3. GLOBAL PROPERTIES

Harris & van den
Bergh (1981)
introduced specific frequency
(SN = NGC ×
100.4(MV + 15)) as a measure of the
richness of a GC system normalized to host galaxy luminosity. This
statistic has been widely used in toy models to assess the feasibility
of galaxy formation mechanisms, e.g., the formation of gEs from
disk-disk mergers. NGC was originally calculated by
doubling the number of GCs brighter than the turnover of the GCLF. This
definition makes both practical and physical sense. The faint end of the
GCLF is usually poorly defined (suffering both contamination and
incompleteness), and ~ 90% of the mass of the GC system resides in the
bright half. This approach is implicit when fitting a Gaussian (or
t5) functions to observed GCLFs, since observations
rarely sample the faintest clusters.

SN comparisons among galaxies are only valid if
all galaxies have the same stellar mass-to-light (M/L) ratios. For this
reason,
Zepf & Ashman (1993)
introduced the quantity T - the
number of GCs per 109M of galaxy stellar
mass. Since M/L is not generally known in detail for a particular
galaxy, it is usually applied as a scaling factor that is different for
each galaxy type, e.g., stellar M/LV = 10 for Es
and 5 for Sbc galaxies like the Galaxy. In this section we quote
observational results in terms of SN, but
convert to T for comparisons among galaxies. An even better
approach would be to directly estimate stellar masses for individual
galaxies.
Olsen et al. (2004)
discuss the use of K-band magnitudes for this purpose.

Soon after the merger model was proposed,
van den Bergh (1982)
argued that elliptical galaxies could not arise from the merger of spiral
galaxies, since spirals have systematically lower
SN values than ellipticals.
Schweizer (1987)
and Ashman & Zepf
(1992)
suggested that this problem could be solved
if new GCs were formed in the merging process. Observations of large
numbers of YMCs in recent mergers seemed to support this
solution. However, the SN will only increase
through the merger if the GC formation efficiency is higher than it was
when the existing GC system was formed. Studies of YMCs in nearby
spirals
(Larsen & Richtler
2000)
suggest that galaxies with larger
star formation rates have more of their light in young clusters, but it
seems unlikely that local mergers are more efficient at forming GCs than
in the gas-rich, violent early universe (see
Harris 2001).

In recent years there have been few wide-field imaging studies of the
sort needed to accurately estimate
SN. Nonetheless, a trend has emerged that
suggests reconsideration of some earlier results. Newer
SN values tend to be lower than older
ones. This revision stems, for the most part, from improved photometry
that is now deep enough to properly define the GCLF turnover and reject
contaminants. Imaging studies that cover a wide field of view are also
important, because they avoid uncertain extrapolations of spatial
profiles from the inner regions of galaxies. In some cases, like the
Fornax gE NGC 1399, the luminosity of the galaxy was
underestimated. When corrected, the SN value
for this galaxy was revised downward by a factor of two, from
SN ~ 12 to 5-6
(Ostrov et al. 1998;
Dirsch et al. 2003).

It has been argued for some time that the evolutionary histories of
central cluster galaxies are different than other Es of similar
mass. Somehow this special status has resulted in high
SN (or T). In addition, galaxies in
high-density environments tend to have higher
SN than those in groups.
McLaughlin (1999)
argued that high SN values in central galaxies
arise because bound hot gas has been ignored for these galaxies, and
that they do not reflect an increased GC formation efficiency with
respect to other galaxies (see
Blakeslee, Tonry, &
Metzger 1997
for additional arguments in favor of the hypothesis that high
SN is due to large galactic mass-to-light
ratios). The properties of the E galaxy NGC 4636 may also be consistent
with this view. Despite its relatively low-density environment, it has
SN ~ 6, a value typical of central cluster galaxies
(Dirsch et al. 2005).
However, the galaxy has a dark matter halo (traced by a halo of hot
X-ray gas) that is unusually massive for its luminosity.

The classic
Harris (1991)
diagram of SN
vs. luminosity implied a monotonic increase of
SN with galaxy mass for high-mass galaxies;
that diagram also showed an increase toward low luminosities for dwarf
galaxies. Both of these trends are less apparent in newer data. The
situation for dwarf galaxies is discussed in more detail in
Section 10, though
it is worth noting here that it is difficult to make robust estimates of
the number of GCs in low-mass galaxies outside of the Local Group. In
our view, the run of SN with galaxy mass and
environment remains uncertain. Additional discussion may be found in
McLaughlin (1999)
and the reviews by
Elmegreen (1999) and
Harris (2001).

3.1.1 SUBPOPULATIONS
Many of the problems with direct SN comparisons
can be circumvented by considering the metal-poor and metal-rich
subpopulations separately. In particular, recent mergers should only
affect the metal-rich peak; independent of the details of new star
formation, the SN of metal-poor GCs will not increase.
Rhode, Zepf, & Santos
(2005)
have exploited this fact by
studying T for metal-poor GCs in 13 massive nearby galaxies,
nearly equally split between early- and late-type. In
Figure 4 we show
both Tblue and Tred
vs. stellar galaxy mass. The Tblue values
are taken from their paper, and the Tred data
were kindly provided by K. Rhode. Rhode et al. found an overall
correlation between Tblue and galaxy mass. The
spirals are all consistent with Tblue ~ 1,
while cluster Es lie higher at Tblue ~ 2-2.5. NGC 4594 also has Tblue ~ 2 (note in
their classification NGC 4594 is an S0, not an Sa). Other field/group
Es, including NGC 5128, NGC 1052, and NGC 3379, have values similar to
those of the spirals. Since M / LV increases
with galaxy mass (with a relation as steep as
L0.10; e.g.,
Zepf & Silk 1996),
it is reasonable to expect at least a weak
trend of T with galaxy mass. However,
Rhode et al. (2005)
argue that this can account for only ~ 1/3 of the observed trend. Because no
global GC color studies of M87 have been published, this galaxy
was not included in the Rhode et al. study. Its
SN value is ~ 3 times larger than the Virgo gE
NGC 4472
(Harris, Harris & McLaughlin 1998).
If both galaxies have
similar total fractions of metal-poor GCs, the
Tblue value for M87 would be ~ 8, though this
value would be much lower if the mass of its hot gas halo were included
along with the stellar mass
(McLaughlin 1999).

Figure 4.Tblue and
Tred (top and bottom panels, respectively) vs. galaxy
mass for a range of spirals and Es
(Rhode et al. 2005).
Filled squares are cluster Es, open squares are field/group
Es and S0s, open circles are field/group spirals, and the open star is
the Sa/S0 galaxy NGC 4594. There is a general trend of increasing
Tblue and Tred with galaxy mass
(Data courtesy K. Rhode).

Based solely on the metal-poor GCs, these comparisons seem to rule out
the formation of cluster gEs (and some massive Es in lower-density
environments) by major mergers of disk galaxies. However, the relative
roles of galaxy mass and environment are still unclear. Spirals in
clusters like Virgo and Fornax and more massive field/small group Es
remain to be studied in detail. The metal-poor GC subpopulations of some
lower-mass Es in low-density environments are still consistent with
merger formation. The biggest caveat to these interpretations is the
effect of biasing - that structure formation is not
self-similar. Present-day spirals are mostly located in low-density
environments like loose groups and the outskirts of
clusters. High-Tblue disk galaxies may have been
common in the central regions of proto-galaxy clusters at high redshift
but have merged themselves out of existence (or could, in some cases,
have been converted to S0s) by the present day.
Rhode et al. (2005)
argue that the observed trend of high Tblue for
cluster galaxies might be expected in hierarchical structure formation,
since halos in high-density environments will collapse and form
metal-poor GCs first (see also
West 1993).
If GC formation is then
truncated (by reionization, for example), such halos will have a larger
number of metal-poor GCs than similar mass halos in lower density
environments. See Section 11 for additional
discussion of biasing.

The Tred data show a similar correlation with galaxy
mass, although with a smaller dynamic range. Note that the
Tred values for the spirals (~ 0.5-1) are normalized
to the total galaxy mass in stars. Most have bulge-to-total
ratios of < 0.3, so if Tred had been normalized
just to the spheroidal component, it would be substantially higher than
plotted. These data appear consistent with the hypothesis of
near-constant formation efficiency for metal-rich GCs in both spirals
and field Es with respect to spheroidal stellar mass
(Forbes, Brodie, &
Larsen 2001;
see also
Kissler-Patig et al. 1997).
The massive
cluster Es have both higher Tred and
Tblue. Again, however, because of the sample under
study (with few field Es and no cluster spirals), it is unclear whether
environment or mass is the predominating influence. This distinction is
moot for the most massive Es since they are found almost exclusively in
clusters, but is still relevant for typical Es.

Estimating the spread in Tred at a given galaxy mass
should help constrain the star-formation histories of early-type
galaxies. The stellar mass of an E might have been built entirely
through violent, gas-rich mergers (with metal-rich GC formation), or,
alternatively, many of the stars could instead have formed quiescently
in mature spiral disks (with little metal-rich GC formation).
Tred for the latter E should be significantly lower
than for the former E.

Most of the existing information on the global spatial distributions of
GCs dates from older studies that could not separate GCs into
subpopulations. The projected radial distributions are often fitted with
power laws over a restricted range in radius, and it is clear that more
luminous galaxies have shallower radial distributions
(Harris 1986;
see the compilation in
Ashman & Zepf 1998).
Considering the GC system as
a whole, typical projected power law indices range from ~ -2 to -2.5 for
some low-luminosity Es (this is also a good fit to the Galactic GC system;
Harris 2001)
to ~ -1.5 or a bit lower for the most massive
gEs. However, it should be kept in mind that power laws provide a poor
fit over the entire radial range. Most GC radial distributions have
cores, and gradually become steeper in their outer parts. King models
capture some of this behavior. In nearly all cases, the GCs have a more
extended spatial distribution than the galaxy field stars.

There have been a few wide field imaging programs which considered GC
subpopulations separately. In their study of the Virgo gE NGC 4472,
Geisler et al. (1996)
were the first to show clearly that color
gradients in GC systems are driven solely by the different radial
distributions of the subpopulations. The metal-poor and metal-rich GCs
themselves show no radial color gradients.
Rhode & Zepf (2001)
found a color gradient for the total GC system in NGC 4472 interior to ~
8', but no gradient when the full radial extent of the
GC system (22' ~ 110 kpc) was considered.
Dirsch et al. (2003)
studied the GC system of the Fornax gE NGC 1399 out to ~
25'(~ 135 kpc); this work was extended to larger radii by
Bassino et al. (2006).
The radial distributions of the two
subpopulations are shown in Figure 5, along with
the profile of the
galaxy itself. The metal-poor and metal-rich subpopulations have power
law slopes of ~ -1.6 and ~ -1.9, respectively. These differences persist
to large radii, and lead to an overall color gradient in the GC
system. The radial distribution of the metal-rich GCs is a close match
to that of the galaxy light, and suggests that they formed
contemporaneously.

Figure 5. Radial surface density
distribution of metal-poor (open circles) and metal-rich (filled
circles) GCs in the Fornax gE NGC 1399. The solid line is the scaled
galaxy light profile in the R-band. The metal-rich GCs are more
centrally concentrated, and closely follow the underlying galaxy
light. The radial distribution of the metal-poor GCs is flatter; they
dominate the GC system at large radii
(Bassino et
al. 2006).

Another notable finding is the rather abrupt truncation of GC systems at
large galactocentric radius.
Rhode & Zepf (2001)
found that the surface density of GCs in NGC 4472 falls off faster than a de
Vaucoleurs or power law fit at ~ 20'(~ 100 kpc). A
similar drop-off occurs at 11' in NGC 4406
(Rhode & Zepf 2004),
and at 9' in NGC 4636
(Dirsch et al. 2005).
This may be evidence of truncation by the tidal field of the cluster.

Dissipationless mergers (whether disk-disk or E-E) tend to flatten the
radial slopes of existing GC systems and create central cores
(Bekki & Forbes 2005).
These cores are observed and have sizes of a few kpc
(Forbes et al. 1996).
These results apply to pre-existing GCs, which
certainly includes metal-poor GCs, as well as metal-rich GCs that
existed before the merger. Thus, the trends predicted by the Bekki &
Forbes simulation appear qualitatively consistent with observations. The
observations are also consistent with more extensive merger histories
for more massive galaxies; these gradually produce larger cores and
flatter GC radial distributions. A desirable extension to this work
would be to place these simulations in a cosmological framework in which
merging occurs according to a full N-body merger tree. Also, as data
become available, comparisons between observations and simulations could
be restricted to metal-poor GCs. With this approach, any new metal-rich
GCs that might have formed in the merger are irrelevant.

Ashman & Zepf (1998)
noted that little was known about the
two-dimensional spatial distributions of GC systems. Scant progress has
been made in the intervening years. Existing data are consistent with
the hypothesis that both subpopulations have ellipticities and position
angles similar to those of the spheroids of their parent galaxies (e.g.,
NGC 1427,
Forte et al. 2001;
NGC 1399,
Dirsch et al. 2003;
NGC 4374,
Gómez & Richtler
2004;
NGC 4636,
Dirsch et al. 2005).
This also holds for the dEs in the Local Group
(Minniti et al. 1996).
It may be that in some galaxies (e.g., the E4 NGC 1052;
Forbes, Georgakakis, &
Brodie 2001)
the metal-rich GCs follow the galaxy ellipticity more
closely than the metal-poor GCs, but whether this is a common phenomenon
is unknown. Naively, if the metal-rich GCs formed along with the bulk of
the galaxy field stars, they should closely trace the galaxy light. The
spatial distribution of the metal-poor GCs will depend in detail upon
the assembly history of the galaxy.

3.3.1. SPIRALS Our views on the GC
systems of spiral galaxies are heavily shaped by the properties of the
Milky Way (and, to a lesser degree, M31). This is discussed in detail in
Section 5. A principal result from the Galaxy
is that the metal-poor and metal-rich GCs are primarily associated with
the halo and bulge, respectively.
Forbes et al. (2001)
introduced the idea that the bulge
GCs in spirals are analogous to the "normal" metal-rich GCs in
early-type galaxies, and that in both spirals and field Es the
metal-rich GCs have SN ~ 1 when normalized solely to
the bulge luminosity. The constancy of bulge SN
appeared consistent with observations of a rather small set of galaxies
(Milky Way, M31, M33, NGC 4594) but needed further testing.

Goudfrooij et al. (2003)
provided such a test with an HST/WFPC2
imaging study of seven edge-on spirals, ranging across the Hubble
sequence (the previously-studied NGC 4594 was part of the
sample). Edge-on galaxies were chosen to minimize the effects of dust
and background inhomogeneities on GC detection. Corrections for spatial
coverage were carried out by comparison to the Galactic GC system; this
does not appear to introduce systematic errors (see Goudfrooij et
al. for additional discussion).
Kissler-Patig et
al. (1999)
had previously found that one of these galaxies, NGC 4565, has a total
number of GCs similar to the Galaxy. The small WFPC2 field of view and
the low SN (or T) values of spirals as compared
to Es resulted in the detection of only tens of GCs in some of the
Goudfrooij et al. galaxies. While bimodality was not obvious in all of
the color distributions, each galaxy had GCs with a range of colors,
consistent with multiple subpopulations. Using a color cut to divide the
samples into metal-poor and metal-rich GCs, Goudfrooij et al. found that
all of the galaxies in their study had (i) a subpopulation of metal-poor
GCs with SN ~ 0.5-0.6 (normalized to total galaxy
light), and (ii) constant bulge SN, with the exception
of the rather low-luminosity Sa galaxy NGC 7814, which appeared to have
few GCs of any color. NGC 7814 was later the target of a ground-based
study by
Rhode & Zepf (2003)
with the WIYN telescope. They found a
significant metal-rich GC subpopulation with a bulge
SN squarely in the middle of the range found for the
other galaxies, which showed that the single WFPC2 pointing on the
sparse GC system of NGC 7814 gave an incomplete picture of the
galaxy. In this case even small radial leverage was important: Rhode
& Zepf found that the surface density of GCs dropped to zero at just
12 kpc (3') projected.

Chandar, Whitmore, &
Lee (2004)
studied GCs in five nearby spirals. Their galaxies (e.g., M51, M81) tended to be closer and
generally better-studied than those in the Goudfrooij et al. sample, but
they were also at less favorable inclination angles. As a result, their
GC candidate samples were more prone to contamination and more affected
by (sometimes unknown amounts of) reddening. This was partially
mitigated by their wide wavelength coverage, including (in some cases)
U-band imaging, to help constrain the reddening of individual
GCs. Chandar et al. found evidence for bimodal GC color distributions in
M81 and M101. Interestingly, M51, which had rather deep imaging, showed
no evidence for metal-rich GCs. They found that NGC 6946 and M101 had
subpopulations of clusters with sizes similar to GCs but extending to
fainter magnitudes; the typical log-normal GCLF was not seen. In
NGC 6946 the imaging was quite shallow and these
faint objects were found to be blue, suggesting that they might be
contaminants. However, in M101
the imaging was deeper and the faint objects had red colors, consistent
with old stellar populations. This may be evidence that some spirals
possess clusters unlike those typical of Es, and these clusters may be
related to the faint red objects seen in some S0s (see next
subsection). Chandar et al. also compiled data from the literature on
the GC systems of spirals, and argued that SN / T
depends on Hubble type, but not on galaxy mass. This is consistent with
the findings of
Goudfrooij et al. (2003).

In principle, the SN value should depend on whether a
particular bulge formed "classically", with intense star formation, or
through secular processes in quiescent gas disks (e.g.,
Kormendy & Kennicutt
2004).
In the former case we might expect a bulge
SN similar to that found for Es, but in the latter
case the star formation is likely to be sufficiently slow and extended
that few or no GCs are formed along with the bulge stars. This may
result in a rather low bulge SN compared to Es of
similar mass. The implication is that all the bulges of galaxies in the
Goudfrooij et al. sample formed predominantly through the "classical"
route. The generally old ages of the metal-rich GCs in spirals (see
Section 4)
is evidence that the majority of bulge star formation, by whatever
mechanism, happened at relatively early epochs.

Kormendy & Kennicutt
(2004)
argue that a large fraction of spiral
bulges are built by secular evolution, and that these "pseudobulges" are
especially common in late-type spirals. The diagnostics for pseudobulges
are many, but include cold kinematics, surface brightness profiles with
low Sersic indices, and, in some cases, young stellar populations. It is
worth emphasizing that many of these pseudobulges could be composite
bulges with young to intermediate-age stars superposed on an old
classical bulge. In this case, the bulge SN could
serve as a diagnostic of the degree to which a given bulge can have been
built by classical or secular processes. The Milky Way itself could be
an example of such a bulge. Its bulge is dominated by an old stellar
population, but has a rather low velocity dispersion for its mass. The
kinematics of the metal-rich GCs could be consistent with association
with either a bulge or a bar
(Côté 1999).

3.3.2 S0s
The leading theory for the formation of most S0s involves their
transformation from spirals as groups and clusters virialize (e.g.,
Dressler et al. 1997).
This can occur in a variety of ways, including ram pressure stripping
and minor mergers that disrupt the disk sufficiently to halt star
formation. In
this context, it may be more appropriate to compare the GC systems of
S0s to those of spirals, rather than make the traditional comparison
with Es. Nonetheless, the GC systems of S0s appear to be quite similar
to those of Es when compared at fixed mass.
Kundu & Whitmore
(2001b)
studied a variety of S0s with WFPC2 snapshot imaging, and in many
galaxies found broad color distributions consistent with multiple
subpopulations.
Peng et al. (2006b)
used deeper imaging from the ACS
Virgo Cluster Survey and found color bimodality in nearly all of the
massive S0s in their sample. These S0s fall right on the GC color-galaxy
luminosity relations of the Es. If indeed S0s descend from spirals, this
is yet another piece of evidence that massive galaxies of all types
along the Hubble sequence have very similar GC color distributions, and
hence are likely to have experienced similar violent formation processes
at some point in their history.

One interesting finding so far confined to S0s was the serendipitous
discovery of a new class of star cluster, now known informally as the
Faint Fuzzies (FFs). These objects were first detected in the nearby (10
Mpc) S0 NGC 1023. Along with a normal, bimodal system of
compact GCs, this galaxy hosts an additional population of faint
(MV > -7) extended (Reff ~
7-15 pc) star clusters. In deep HST/WFPC2 images, these objects
are confined to an annular distribution closely corresponding to the
galaxy's isophotes
(Larsen & Brodie
2000).
Spectroscopic follow-up
with Keck/LRIS showed that the FFs are metal-rich ([Fe/H] ~ -0.5), old
(> 8 Gyr), and rotating in the disk of the galaxy
(Brodie & Larsen
2002).
With old ages, inferred masses of
105M, and
sizes ~ 5 times larger than a typical globular or open cluster, these
objects occupy a distinct region of age-size-mass parameter space for
star clusters. As a population, they have no known analogs in the Milky
Way or elsewhere in the Local Group. Similar objects have been found in
the S0 galaxy NGC 3384
(Brodie & Larsen 2002)
and NGC 5195, a barred S0 interacting with M51
(Lee, Chandar & Whitmore 2005;
Hwang & Lee 2006).
Peng et al. (2006)
found FFs in ~ 25% of the S0s in the ACS
Virgo Cluster Survey. Due to biases in sample selection, however, this
fraction is probably not yet well-constrained. The FFs have relatively
low surface brightness, and their properties may be consistent with
MR2 (unlike GCs, which show no M - R
relation). In some cases, their colors are redder than those of the
metal-rich GCs in the same galaxy, which may suggest higher metallicities.

Brodie, Burkert, & Larsen (2004)
and Burkert, Brodie &
Larsen (2005)
showed that the properties of the FFs in NGC 1023 were consistent
with having formed in a rotating ring-like structure and explored their
origin. Numerical simulations suggest that objects with the sizes and
masses of FFs can form inside giant molecular clouds, provided star
formation occurs only when a density threshold is exceeded. Such special
star forming conditions may be present during specific galaxy-galaxy
interactions, in which one galaxy passes close to the center of a disk
galaxy, precipitating a ring of star formation. They speculated that the
FFs might then be signposts for the transformation of spiral galaxies
into lenticulars via such interactions. Alternatively, such conditions
might also occur in the inner resonance rings associated with the bars
at the centers of disk galaxies. In this case, the old ages of the FFs
would suggest that barred disks must have been present at early times.